What is sqrt(2x^3)*sqrt(18x^5) ?

The solution to sqrt(2x^3)*sqrt(18x^5) is 6x^4

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simplify sqrt(2x^3)*sqrt(18x^5)

simplify

2 x^{3} \cdot 18 x^{5}

6 x^{4}

Solution steps

2 x^{3} 18 x^{5}

Simplify

2 x^{3} : 2 x x

= 2 x x 18 x^{5}

Simplify

18 x^{5} : 32 x^{2} x

= 2 x x \cdot 32 x^{2} x

Apply radical rule:

a a = a, a \geq 0

22 = 2

= 2 x x \cdot 3 x^{2} x

Apply radical rule:

a a = a,

assuming

a \geq 0

x x = x

= 2 xx \cdot 3 x^{2}

Multiply the numbers:

2 \cdot 3 = 6

= 6 xx x^{2}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

xx x^{2} = x^{1 + 1 + 2}

= 6 x^{1 + 1 + 2}

Add the numbers:

1 + 1 + 2 = 4

= 6 x^{4}

\frac{5 i}{6 + 8 i}

\frac{2}{- 2 - 5 2}

(k x)^{2}

\frac{b ^{3} - a ^{3}}{3 ( b - a )}

(3 x - y)^{5}